Disclaimer: Please note that this web site is still under developement and some data may be not fully validated or incomplete!
Comparison of manipulation results
NK-Index, coalition k = 1, number of alternatives m = 3
| Rules | IC | IAC | ||||||
|---|---|---|---|---|---|---|---|---|
| Leximin | Leximax | Risk-averse | Risk-lover | Leximin | Leximax | Risk-averse | Risk-lover | |
| Plurality Rule | Coalitional Manipulation vs. Individual Manipulation 0.00182 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00165 > 0.01 0/98 > 0.001 5/98 Individual Manipulation vs. Exact Coalitional 2025 0.00106 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.0018 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00165 > 0.01 0/98 > 0.001 5/98 Individual Manipulation vs. Exact Coalitional 2025 0.00106 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00182 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00165 > 0.01 0/98 > 0.001 5/98 Individual Manipulation vs. Exact Coalitional 2025 0.00106 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.0018 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00165 > 0.01 0/98 > 0.001 5/98 Individual Manipulation vs. Exact Coalitional 2025 0.00106 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 |
| Approval q=2 | Coalitional Manipulation vs. Individual Manipulation 0.00253 > 0.01 0/39 > 0.001 15/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 26/98 Individual Manipulation vs. Exact Coalitional 2025 0.00226 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Individual Manipulation 0.00196 > 0.01 0/39 > 0.001 11/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 26/98 Individual Manipulation vs. Exact Coalitional 2025 0.00118 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00253 > 0.01 0/39 > 0.001 15/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 26/98 Individual Manipulation vs. Exact Coalitional 2025 0.00226 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Individual Manipulation 0.00196 > 0.01 0/39 > 0.001 11/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 26/98 Individual Manipulation vs. Exact Coalitional 2025 0.00118 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 |
| Inverse Plurality | Coalitional Manipulation vs. Individual Manipulation 0.00253 > 0.01 0/39 > 0.001 15/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 26/98 Individual Manipulation vs. Exact Coalitional 2025 0.00226 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Individual Manipulation 0.00196 > 0.01 0/39 > 0.001 11/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 26/98 Individual Manipulation vs. Exact Coalitional 2025 0.00118 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00253 > 0.01 0/39 > 0.001 15/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 26/98 Individual Manipulation vs. Exact Coalitional 2025 0.00226 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Individual Manipulation 0.00196 > 0.01 0/39 > 0.001 11/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 26/98 Individual Manipulation vs. Exact Coalitional 2025 0.00118 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 |
| Borda's Rule | Coalitional Manipulation vs. Individual Manipulation 0.00181 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00145 > 0.01 0/98 > 0.001 8/98 Individual Manipulation vs. Exact Coalitional 2025 0.0011 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00336 > 0.01 0/39 > 0.001 7/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00139 > 0.01 0/98 > 0.001 9/98 Individual Manipulation vs. Exact Coalitional 2025 0.00273 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00181 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00145 > 0.01 0/98 > 0.001 8/98 Individual Manipulation vs. Exact Coalitional 2025 0.0011 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00336 > 0.01 0/39 > 0.001 7/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00139 > 0.01 0/98 > 0.001 9/98 Individual Manipulation vs. Exact Coalitional 2025 0.00273 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00135 > 0.01 0/98 > 0.001 1/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00098 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00135 > 0.01 0/98 > 0.001 1/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00098 > 0.01 0/98 > 0.001 0/98 |
| Black's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00222 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00103 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.00188 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0035 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00064 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00326 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0038 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00103 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.00362 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00191 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00065 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00152 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00059 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00058 > 0.01 0/98 > 0.001 0/98 |
| Minimal dominant set | Coalitional Manipulation vs. Individual Manipulation 0.00312 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00075 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00281 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00317 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00099 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00271 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Individual Manipulation 0.00216 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00091 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00203 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00177 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00087 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00157 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00073 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00067 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00084 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 |
| Minimal undominated set | Coalitional Manipulation vs. Individual Manipulation 0.00222 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00075 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00188 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0035 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00326 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.0038 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.0008 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00362 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00191 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00152 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 |
| Minimal weakly stable set | Coalitional Manipulation vs. Individual Manipulation 0.00222 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00075 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00188 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0035 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00326 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.0038 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.0008 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00362 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00191 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00152 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 |
| Fishburn’s Rule | Coalitional Manipulation vs. Individual Manipulation 0.00222 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00075 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00188 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0035 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00326 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.0038 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.0008 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00362 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00191 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00152 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 |
| Uncovered set I | Coalitional Manipulation vs. Individual Manipulation 0.00176 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00118 > 0.01 0/98 > 0.001 2/98 Individual Manipulation vs. Exact Coalitional 2025 0.0012 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00246 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00117 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.00168 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Individual Manipulation 0.00157 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00113 > 0.01 0/98 > 0.001 3/98 Individual Manipulation vs. Exact Coalitional 2025 0.00144 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00277 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00117 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.00203 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00083 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00087 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00087 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00083 > 0.01 0/98 > 0.001 0/98 |
| Uncovered set II | Coalitional Manipulation vs. Individual Manipulation 0.00142 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00088 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00195 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00287 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00079 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00258 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00287 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00079 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00258 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00142 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00088 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00195 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00056 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00068 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00068 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 |
| Richelson | Coalitional Manipulation vs. Individual Manipulation 0.00176 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00118 > 0.01 0/98 > 0.001 2/98 Individual Manipulation vs. Exact Coalitional 2025 0.0012 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00246 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00117 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.00168 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Individual Manipulation 0.00157 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00113 > 0.01 0/98 > 0.001 3/98 Individual Manipulation vs. Exact Coalitional 2025 0.00144 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00277 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00117 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.00203 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00083 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00087 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00087 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00083 > 0.01 0/98 > 0.001 0/98 |
| Copeland’s rule I | Coalitional Manipulation vs. Individual Manipulation 0.00278 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00099 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00179 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00433 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00087 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00355 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00278 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00099 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00179 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00433 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00087 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00355 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00043 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00043 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 |
| Copeland’s rule II | Coalitional Manipulation vs. Individual Manipulation 0.00176 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00118 > 0.01 0/98 > 0.001 2/98 Individual Manipulation vs. Exact Coalitional 2025 0.0012 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00246 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00117 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.00168 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Individual Manipulation 0.00157 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00113 > 0.01 0/98 > 0.001 3/98 Individual Manipulation vs. Exact Coalitional 2025 0.00144 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00277 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00117 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.00203 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00083 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00087 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00087 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00083 > 0.01 0/98 > 0.001 0/98 |
| Copeland’s rule III | Coalitional Manipulation vs. Individual Manipulation 0.00222 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00075 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00188 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0035 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00326 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.0038 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.0008 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00362 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00191 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00152 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 |
| Simpson’s Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00222 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.001 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00188 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0035 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00073 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00326 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0038 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.001 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00362 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00191 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.0007 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00152 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00054 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00053 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00054 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00054 > 0.01 0/98 > 0.001 0/98 |
| MinMax procedure | Coalitional Manipulation vs. Individual Manipulation 0.00222 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.001 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00188 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0035 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00073 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00326 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0038 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.001 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00362 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00191 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.0007 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00152 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00054 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00053 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00054 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00054 > 0.01 0/98 > 0.001 0/98 |
| Strong q-Paretian simple majority | Coalitional Manipulation vs. Individual Manipulation 0.00153 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00103 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.00091 > 0.01 0/39 > 0.001 0/39 | Coalitional Manipulation vs. Individual Manipulation 0.00108 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00053 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00063 > 0.01 0/39 > 0.001 0/39 | Coalitional Manipulation vs. Individual Manipulation 0.00132 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00081 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00091 > 0.01 0/39 > 0.001 0/39 | Coalitional Manipulation vs. Individual Manipulation 0.00175 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00113 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00055 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.001 > 0.01 0/98 > 0.001 1/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00093 > 0.01 0/98 > 0.001 0/98 |
| Strong q-Paretian plurality | Coalitional Manipulation vs. Individual Manipulation 0.00199 > 0.01 0/39 > 0.001 12/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 27/98 Individual Manipulation vs. Exact Coalitional 2025 0.00105 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00199 > 0.01 0/39 > 0.001 10/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 28/98 Individual Manipulation vs. Exact Coalitional 2025 0.0012 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00199 > 0.01 0/39 > 0.001 12/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 27/98 Individual Manipulation vs. Exact Coalitional 2025 0.00105 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00199 > 0.01 0/39 > 0.001 10/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00227 > 0.01 0/98 > 0.001 28/98 Individual Manipulation vs. Exact Coalitional 2025 0.0012 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00088 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00085 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00088 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00085 > 0.01 0/98 > 0.001 0/98 |
| Strongest q-Paretian simple majority | Coalitional Manipulation vs. Individual Manipulation 0.00222 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00075 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00188 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0035 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00326 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.0038 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.0008 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00362 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00191 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00152 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 |
| Threshold Rule | Coalitional Manipulation vs. Individual Manipulation 0.00321 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00192 > 0.01 0/98 > 0.001 12/98 Individual Manipulation vs. Exact Coalitional 2025 0.00322 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Individual Manipulation 0.00339 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00192 > 0.01 0/98 > 0.001 13/98 Individual Manipulation vs. Exact Coalitional 2025 0.00361 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Individual Manipulation 0.00321 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00192 > 0.01 0/98 > 0.001 12/98 Individual Manipulation vs. Exact Coalitional 2025 0.00322 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Individual Manipulation 0.00339 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00192 > 0.01 0/98 > 0.001 13/98 Individual Manipulation vs. Exact Coalitional 2025 0.00361 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00083 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00078 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00083 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00078 > 0.01 0/98 > 0.001 0/98 |
| Nanson's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00224 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00073 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00191 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.0027 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.0007 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00246 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00248 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00075 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.0023 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00246 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.0007 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00207 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00047 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00041 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00045 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00042 > 0.01 0/98 > 0.001 0/98 |
| Inverse Borda's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00224 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00085 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00191 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.0027 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00071 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00246 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00248 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.0008 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.0023 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00246 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00207 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00046 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00041 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00044 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00043 > 0.01 0/98 > 0.001 0/98 |
| Hare's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.0015 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00108 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.00105 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0012 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00084 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00074 > 0.01 0/39 > 0.001 0/39 | Coalitional Manipulation vs. Individual Manipulation 0.00132 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00113 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.00105 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00115 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00084 > 0.01 0/98 > 0.001 0/98 Individual Manipulation vs. Exact Coalitional 2025 0.00074 > 0.01 0/39 > 0.001 0/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00063 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00071 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00063 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00061 > 0.01 0/98 > 0.001 0/98 |
| 1-stable set | Coalitional Manipulation vs. Exact Coalitional 2025 0.00089 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00137 > 0.01 0/98 > 0.001 1/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00075 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00114 > 0.01 0/98 > 0.001 1/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00074 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00073 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 |
| 2-stable set | Coalitional Manipulation vs. Exact Coalitional 2025 0.00075 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.0008 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 |
| 3-stable set | Coalitional Manipulation vs. Exact Coalitional 2025 0.00075 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.0008 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00077 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00039 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00057 > 0.01 0/98 > 0.001 0/98 |
| Coombs' Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00143 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00101 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.0011 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.0016 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00113 > 0.01 0/98 > 0.001 3/98 Individual Manipulation vs. Exact Coalitional 2025 0.00113 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00143 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00101 > 0.01 0/98 > 0.001 1/98 Individual Manipulation vs. Exact Coalitional 2025 0.0011 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.0016 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Exact Coalitional 2025 0.00115 > 0.01 0/98 > 0.001 4/98 Individual Manipulation vs. Exact Coalitional 2025 0.00113 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00055 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00056 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00055 > 0.01 0/98 > 0.001 0/98 | Coalitional Manipulation vs. Exact Coalitional 2025 0.00055 > 0.01 0/98 > 0.001 0/98 |
NK-Index, coalition k = 1, number of alternatives m = 4
| Rules | IC | IAC | ||||||
|---|---|---|---|---|---|---|---|---|
| Leximin | Leximax | Risk-averse | Risk-lover | Leximin | Leximax | Risk-averse | Risk-lover | |
| Plurality Rule | Coalitional Manipulation vs. Individual Manipulation 0.0014 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Coalitional 2025 0.00192 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.0026 > 0.01 0/39 > 0.001 7/39 | Coalitional Manipulation vs. Individual Manipulation 0.0014 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Coalitional 2025 0.00183 > 0.01 0/54 > 0.001 9/54 Individual Manipulation vs. Coalitional 2025 0.00259 > 0.01 0/39 > 0.001 7/39 | Coalitional Manipulation vs. Coalitional 2025 0.00132 > 0.01 0/56 > 0.001 4/56 | Coalitional Manipulation vs. Coalitional 2025 0.00128 > 0.01 0/56 > 0.001 3/56 | ||||
| Approval q=2 | Coalitional Manipulation vs. Individual Manipulation 0.00142 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Coalitional 2025 0.0019 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.00194 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Individual Manipulation 0.00154 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Coalitional 2025 0.00159 > 0.01 0/54 > 0.001 5/54 Individual Manipulation vs. Coalitional 2025 0.0016 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.00181 > 0.01 0/56 > 0.001 6/56 | Coalitional Manipulation vs. Coalitional 2025 0.00172 > 0.01 0/56 > 0.001 5/56 | ||||
| Inverse Plurality | Coalitional Manipulation vs. Coalitional 2025 0.00171 > 0.01 0/54 > 0.001 2/54 | Coalitional Manipulation vs. Coalitional 2025 0.00163 > 0.01 0/54 > 0.001 5/54 | Coalitional Manipulation vs. Coalitional 2025 0.00211 > 0.01 0/56 > 0.001 5/56 | Coalitional Manipulation vs. Coalitional 2025 0.00201 > 0.01 0/56 > 0.001 8/56 | ||||
| Borda's Rule | Coalitional Manipulation vs. Individual Manipulation 0.00146 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00168 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00172 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Individual Manipulation 0.00139 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00171 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00172 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Coalitional 2025 0.00215 > 0.01 0/56 > 0.001 6/56 | Coalitional Manipulation vs. Coalitional 2025 0.00224 > 0.01 0/56 > 0.001 6/56 | ||||
| Black's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00148 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Coalitional 2025 0.0015 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00175 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Individual Manipulation 0.00149 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.00146 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.00179 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Coalitional 2025 0.00154 > 0.01 0/56 > 0.001 6/56 | Coalitional Manipulation vs. Coalitional 2025 0.0016 > 0.01 0/56 > 0.001 6/56 | ||||
| Minimal dominant set | Coalitional Manipulation vs. Individual Manipulation 0.00146 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.0015 > 0.01 0/54 > 0.001 11/54 Individual Manipulation vs. Coalitional 2025 0.0022 > 0.01 0/39 > 0.001 8/39 | Coalitional Manipulation vs. Individual Manipulation 0.00123 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Coalitional 2025 0.0017 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00136 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Coalitional 2025 0.0014 > 0.01 0/56 > 0.001 4/56 | Coalitional Manipulation vs. Coalitional 2025 0.00168 > 0.01 0/56 > 0.001 6/56 | ||||
| Minimal undominated set | Coalitional Manipulation vs. Coalitional 2025 0.27908 > 0.01 52/54 > 0.001 53/54 | Coalitional Manipulation vs. Coalitional 2025 0.22684 > 0.01 53/54 > 0.001 53/54 | Coalitional Manipulation vs. Coalitional 2025 0.20506 > 0.01 54/56 > 0.001 55/56 | Coalitional Manipulation vs. Coalitional 2025 0.21529 > 0.01 55/56 > 0.001 55/56 | ||||
| Minimal weakly stable set | Coalitional Manipulation vs. Coalitional 2025 0.00144 > 0.01 0/54 > 0.001 7/54 | Coalitional Manipulation vs. Coalitional 2025 0.00854 > 0.01 0/54 > 0.001 26/54 | Coalitional Manipulation vs. Coalitional 2025 0.00177 > 0.01 0/56 > 0.001 4/56 | Coalitional Manipulation vs. Coalitional 2025 0.00656 > 0.01 0/56 > 0.001 31/56 | ||||
| Fishburn’s Rule | Coalitional Manipulation vs. Coalitional 2025 0.00151 > 0.01 0/54 > 0.001 4/54 | Coalitional Manipulation vs. Coalitional 2025 0.00154 > 0.01 0/54 > 0.001 6/54 | Coalitional Manipulation vs. Coalitional 2025 0.00162 > 0.01 0/56 > 0.001 4/56 | Coalitional Manipulation vs. Coalitional 2025 0.00182 > 0.01 0/56 > 0.001 8/56 | ||||
| Uncovered set I | Coalitional Manipulation vs. Individual Manipulation 0.00094 > 0.01 0/39 > 0.001 0/39 Coalitional Manipulation vs. Coalitional 2025 0.00153 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.00139 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Individual Manipulation 0.00107 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00167 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00141 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.00153 > 0.01 0/56 > 0.001 5/56 | Coalitional Manipulation vs. Coalitional 2025 0.00175 > 0.01 0/56 > 0.001 6/56 | ||||
| Uncovered set II | Coalitional Manipulation vs. Individual Manipulation 0.00155 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Coalitional 2025 0.00184 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.0021 > 0.01 0/39 > 0.001 7/39 | Coalitional Manipulation vs. Individual Manipulation 0.0014 > 0.01 0/39 > 0.001 7/39 Coalitional Manipulation vs. Coalitional 2025 0.00162 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00205 > 0.01 0/39 > 0.001 8/39 | Coalitional Manipulation vs. Coalitional 2025 0.00153 > 0.01 0/56 > 0.001 3/56 | Coalitional Manipulation vs. Coalitional 2025 0.00176 > 0.01 0/56 > 0.001 7/56 | ||||
| Richelson | Coalitional Manipulation vs. Individual Manipulation 0.00095 > 0.01 0/39 > 0.001 0/39 Coalitional Manipulation vs. Coalitional 2025 0.00151 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.00139 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Individual Manipulation 0.00113 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.00183 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00141 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.00147 > 0.01 0/56 > 0.001 5/56 | Coalitional Manipulation vs. Coalitional 2025 0.00178 > 0.01 0/56 > 0.001 7/56 | ||||
| Copeland’s rule I | Coalitional Manipulation vs. Individual Manipulation 0.00146 > 0.01 0/39 > 0.001 7/39 Coalitional Manipulation vs. Coalitional 2025 0.0019 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.0016 > 0.01 0/39 > 0.001 8/39 | Coalitional Manipulation vs. Individual Manipulation 0.00151 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00162 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00214 > 0.01 0/39 > 0.001 9/39 | Coalitional Manipulation vs. Coalitional 2025 0.00209 > 0.01 0/56 > 0.001 4/56 | Coalitional Manipulation vs. Coalitional 2025 0.00205 > 0.01 0/56 > 0.001 9/56 | ||||
| Copeland’s rule II | Coalitional Manipulation vs. Individual Manipulation 0.00124 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.0019 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00167 > 0.01 0/39 > 0.001 7/39 | Coalitional Manipulation vs. Individual Manipulation 0.00143 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Coalitional 2025 0.00185 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.00129 > 0.01 0/39 > 0.001 8/39 | Coalitional Manipulation vs. Coalitional 2025 0.0021 > 0.01 0/56 > 0.001 8/56 | Coalitional Manipulation vs. Coalitional 2025 0.00233 > 0.01 0/56 > 0.001 11/56 | ||||
| Copeland’s rule III | Coalitional Manipulation vs. Individual Manipulation 0.00126 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Coalitional 2025 0.0019 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.0016 > 0.01 0/39 > 0.001 7/39 | Coalitional Manipulation vs. Individual Manipulation 0.00118 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.00138 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00198 > 0.01 0/39 > 0.001 8/39 | Coalitional Manipulation vs. Coalitional 2025 0.00189 > 0.01 0/56 > 0.001 3/56 | Coalitional Manipulation vs. Coalitional 2025 0.002 > 0.01 0/56 > 0.001 9/56 | ||||
| Simpson’s Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00114 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Coalitional 2025 0.00188 > 0.01 0/54 > 0.001 5/54 Individual Manipulation vs. Coalitional 2025 0.00176 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Individual Manipulation 0.00121 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Coalitional 2025 0.0018 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00173 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Coalitional 2025 0.00164 > 0.01 0/56 > 0.001 2/56 | Coalitional Manipulation vs. Coalitional 2025 0.00161 > 0.01 0/56 > 0.001 2/56 | ||||
| MinMax procedure | Coalitional Manipulation vs. Individual Manipulation 0.00114 > 0.01 0/39 > 0.001 1/39 Coalitional Manipulation vs. Coalitional 2025 0.00188 > 0.01 0/54 > 0.001 5/54 Individual Manipulation vs. Coalitional 2025 0.00176 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Individual Manipulation 0.00121 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Coalitional 2025 0.0018 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00173 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Coalitional 2025 0.00164 > 0.01 0/56 > 0.001 2/56 | Coalitional Manipulation vs. Coalitional 2025 0.00161 > 0.01 0/56 > 0.001 2/56 | ||||
| Strong q-Paretian simple majority | Coalitional Manipulation vs. Individual Manipulation 0.00165 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00133 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.00143 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Individual Manipulation 0.00258 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00202 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.00131 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Coalitional 2025 0.00134 > 0.01 0/56 > 0.001 7/56 | Coalitional Manipulation vs. Coalitional 2025 0.00169 > 0.01 0/56 > 0.001 4/56 | ||||
| Strong q-Paretian plurality | Coalitional Manipulation vs. Coalitional 2025 0.0019 > 0.01 0/54 > 0.001 8/54 | Coalitional Manipulation vs. Coalitional 2025 0.00159 > 0.01 0/54 > 0.001 5/54 | Coalitional Manipulation vs. Coalitional 2025 0.00166 > 0.01 0/56 > 0.001 10/56 | Coalitional Manipulation vs. Coalitional 2025 0.00167 > 0.01 0/56 > 0.001 5/56 | ||||
| Strongest q-Paretian simple majority | Coalitional Manipulation vs. Coalitional 2025 0.00143 > 0.01 0/54 > 0.001 6/54 | Coalitional Manipulation vs. Coalitional 2025 0.00156 > 0.01 0/54 > 0.001 6/54 | Coalitional Manipulation vs. Coalitional 2025 0.00181 > 0.01 0/56 > 0.001 3/56 | Coalitional Manipulation vs. Coalitional 2025 0.00211 > 0.01 0/56 > 0.001 5/56 | ||||
| Threshold Rule | Coalitional Manipulation vs. Individual Manipulation 0.0015 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Coalitional 2025 0.00179 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00216 > 0.01 0/39 > 0.001 6/39 | Coalitional Manipulation vs. Individual Manipulation 0.00148 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.00175 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00217 > 0.01 0/39 > 0.001 7/39 | Coalitional Manipulation vs. Coalitional 2025 0.00171 > 0.01 0/56 > 0.001 7/56 | Coalitional Manipulation vs. Coalitional 2025 0.00161 > 0.01 0/56 > 0.001 6/56 | ||||
| Nanson's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00148 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00156 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00148 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Individual Manipulation 0.00126 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00157 > 0.01 0/54 > 0.001 4/54 Individual Manipulation vs. Coalitional 2025 0.00127 > 0.01 0/39 > 0.001 7/39 | Coalitional Manipulation vs. Coalitional 2025 0.00124 > 0.01 0/56 > 0.001 4/56 | Coalitional Manipulation vs. Coalitional 2025 0.00142 > 0.01 0/56 > 0.001 3/56 | ||||
| Inverse Borda's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00156 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.00154 > 0.01 0/54 > 0.001 2/54 Individual Manipulation vs. Coalitional 2025 0.00184 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Individual Manipulation 0.00152 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.00197 > 0.01 0/54 > 0.001 2/54 Individual Manipulation vs. Coalitional 2025 0.00148 > 0.01 0/39 > 0.001 6/39 | Coalitional Manipulation vs. Coalitional 2025 0.00155 > 0.01 0/56 > 0.001 3/56 | Coalitional Manipulation vs. Coalitional 2025 0.00142 > 0.01 0/56 > 0.001 3/56 | ||||
| Hare's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00176 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Coalitional 2025 0.00137 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00208 > 0.01 0/39 > 0.001 6/39 | Coalitional Manipulation vs. Individual Manipulation 0.00176 > 0.01 0/39 > 0.001 9/39 Coalitional Manipulation vs. Coalitional 2025 0.00147 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.00193 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.00184 > 0.01 0/56 > 0.001 4/56 | Coalitional Manipulation vs. Coalitional 2025 0.00201 > 0.01 0/56 > 0.001 4/56 | ||||
| 1-stable set | Coalitional Manipulation vs. Coalitional 2025 0.00168 > 0.01 0/54 > 0.001 7/54 | Coalitional Manipulation vs. Coalitional 2025 0.00173 > 0.01 0/54 > 0.001 8/54 | Coalitional Manipulation vs. Coalitional 2025 0.00111 > 0.01 0/56 > 0.001 3/56 | Coalitional Manipulation vs. Coalitional 2025 0.00178 > 0.01 0/56 > 0.001 10/56 | ||||
| 2-stable set | Coalitional Manipulation vs. Coalitional 2025 0.00136 > 0.01 0/54 > 0.001 4/54 | Coalitional Manipulation vs. Coalitional 2025 0.00154 > 0.01 0/54 > 0.001 7/54 | Coalitional Manipulation vs. Coalitional 2025 0.00165 > 0.01 0/56 > 0.001 4/56 | Coalitional Manipulation vs. Coalitional 2025 0.00175 > 0.01 0/56 > 0.001 7/56 | ||||
| 3-stable set | Coalitional Manipulation vs. Coalitional 2025 0.0015 > 0.01 0/54 > 0.001 5/54 | Coalitional Manipulation vs. Coalitional 2025 0.0015 > 0.01 0/54 > 0.001 10/54 | Coalitional Manipulation vs. Coalitional 2025 0.00167 > 0.01 0/56 > 0.001 6/56 | Coalitional Manipulation vs. Coalitional 2025 0.00168 > 0.01 0/56 > 0.001 7/56 | ||||
| Approval q=3 | Coalitional Manipulation vs. Individual Manipulation 0.00174 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00171 > 0.01 0/54 > 0.001 2/54 Individual Manipulation vs. Coalitional 2025 0.00152 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Individual Manipulation 0.00125 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.00163 > 0.01 0/54 > 0.001 5/54 Individual Manipulation vs. Coalitional 2025 0.00164 > 0.01 0/39 > 0.001 6/39 | Coalitional Manipulation vs. Coalitional 2025 0.00211 > 0.01 0/56 > 0.001 5/56 | Coalitional Manipulation vs. Coalitional 2025 0.00201 > 0.01 0/56 > 0.001 8/56 | ||||
| Coombs' Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00156 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Coalitional 2025 0.00188 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00185 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Individual Manipulation 0.00193 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Coalitional 2025 0.00189 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00185 > 0.01 0/39 > 0.001 8/39 | Coalitional Manipulation vs. Coalitional 2025 0.00125 > 0.01 0/56 > 0.001 7/56 | Coalitional Manipulation vs. Coalitional 2025 0.0014 > 0.01 0/56 > 0.001 7/56 | ||||
NK-Index, coalition k = 1, number of alternatives m = 5
| Rules | IC | IAC | ||||||
|---|---|---|---|---|---|---|---|---|
| Leximin | Leximax | Risk-averse | Risk-lover | Leximin | Leximax | Risk-averse | Risk-lover | |
| Plurality Rule | Coalitional Manipulation vs. Individual Manipulation 0.00165 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00143 > 0.01 0/54 > 0.001 12/54 Individual Manipulation vs. Coalitional 2025 0.0015 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Individual Manipulation 0.0019 > 0.01 0/39 > 0.001 7/39 Coalitional Manipulation vs. Coalitional 2025 0.00156 > 0.01 0/54 > 0.001 11/54 Individual Manipulation vs. Coalitional 2025 0.00155 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Coalitional 2025 0.00204 > 0.01 0/56 > 0.001 8/56 | Coalitional Manipulation vs. Coalitional 2025 0.00204 > 0.01 0/56 > 0.001 8/56 | ||||
| Approval q=2 | Coalitional Manipulation vs. Individual Manipulation 0.00162 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.00185 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.0014 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Individual Manipulation 0.00113 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Coalitional 2025 0.00183 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00148 > 0.01 0/39 > 0.001 7/39 | Coalitional Manipulation vs. Coalitional 2025 0.00114 > 0.01 0/56 > 0.001 3/56 | Coalitional Manipulation vs. Coalitional 2025 0.00107 > 0.01 0/56 > 0.001 2/56 | ||||
| Inverse Plurality | Coalitional Manipulation vs. Individual Manipulation 0.00213 > 0.01 0/39 > 0.001 7/39 Coalitional Manipulation vs. Coalitional 2025 0.00176 > 0.01 0/54 > 0.001 13/54 Individual Manipulation vs. Coalitional 2025 0.00233 > 0.01 0/39 > 0.001 8/39 | Coalitional Manipulation vs. Individual Manipulation 0.00218 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Coalitional 2025 0.00171 > 0.01 0/54 > 0.001 13/54 Individual Manipulation vs. Coalitional 2025 0.00232 > 0.01 0/39 > 0.001 8/39 | Coalitional Manipulation vs. Coalitional 2025 0.00152 > 0.01 0/56 > 0.001 12/56 | Coalitional Manipulation vs. Coalitional 2025 0.00146 > 0.01 0/56 > 0.001 9/56 | ||||
| Borda's Rule | Coalitional Manipulation vs. Individual Manipulation 0.00159 > 0.01 0/39 > 0.001 7/39 Coalitional Manipulation vs. Coalitional 2025 0.00268 > 0.01 0/54 > 0.001 11/54 Individual Manipulation vs. Coalitional 2025 0.00174 > 0.01 0/39 > 0.001 8/39 | Coalitional Manipulation vs. Individual Manipulation 0.00146 > 0.01 0/39 > 0.001 7/39 Coalitional Manipulation vs. Coalitional 2025 0.00268 > 0.01 0/54 > 0.001 10/54 Individual Manipulation vs. Coalitional 2025 0.00174 > 0.01 0/39 > 0.001 9/39 | Coalitional Manipulation vs. Coalitional 2025 0.00176 > 0.01 0/56 > 0.001 9/56 | Coalitional Manipulation vs. Coalitional 2025 0.00176 > 0.01 0/56 > 0.001 8/56 | ||||
| Black's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00147 > 0.01 0/39 > 0.001 2/39 Coalitional Manipulation vs. Coalitional 2025 0.00202 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00145 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00169 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Coalitional 2025 0.002 > 0.01 0/54 > 0.001 5/54 Individual Manipulation vs. Coalitional 2025 0.00162 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Coalitional 2025 0.00149 > 0.01 0/56 > 0.001 9/56 | Coalitional Manipulation vs. Coalitional 2025 0.00157 > 0.01 0/56 > 0.001 7/56 | ||||
| Minimal dominant set | Coalitional Manipulation vs. Individual Manipulation 0.00164 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.00151 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.00138 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00164 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.0016 > 0.01 0/54 > 0.001 10/54 Individual Manipulation vs. Coalitional 2025 0.00128 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.00133 > 0.01 0/56 > 0.001 11/56 | Coalitional Manipulation vs. Coalitional 2025 0.00195 > 0.01 0/56 > 0.001 6/56 | ||||
| Minimal undominated set | Coalitional Manipulation vs. Individual Manipulation 0.48681 > 0.01 38/39 > 0.001 38/39 Coalitional Manipulation vs. Coalitional 2025 0.48656 > 0.01 53/54 > 0.001 54/54 Individual Manipulation vs. Coalitional 2025 0.00116 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.31455 > 0.01 38/39 > 0.001 39/39 Coalitional Manipulation vs. Coalitional 2025 0.31444 > 0.01 53/54 > 0.001 54/54 Individual Manipulation vs. Coalitional 2025 0.00139 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.45925 > 0.01 55/56 > 0.001 55/56 | Coalitional Manipulation vs. Coalitional 2025 0.30705 > 0.01 55/56 > 0.001 56/56 | ||||
| Minimal weakly stable set | Coalitional Manipulation vs. Individual Manipulation 0.00691 > 0.01 0/39 > 0.001 18/39 Coalitional Manipulation vs. Coalitional 2025 0.00727 > 0.01 0/54 > 0.001 28/54 Individual Manipulation vs. Coalitional 2025 0.00122 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.02268 > 0.01 11/39 > 0.001 21/39 Coalitional Manipulation vs. Coalitional 2025 0.02315 > 0.01 12/54 > 0.001 28/54 Individual Manipulation vs. Coalitional 2025 0.00139 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Coalitional 2025 0.0061 > 0.01 0/56 > 0.001 34/56 | Coalitional Manipulation vs. Coalitional 2025 0.02041 > 0.01 10/56 > 0.001 28/56 | ||||
| Fishburn’s Rule | Coalitional Manipulation vs. Individual Manipulation 0.00123 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.00137 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00098 > 0.01 0/39 > 0.001 0/39 | Coalitional Manipulation vs. Individual Manipulation 0.00167 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.0022 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00148 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Coalitional 2025 0.00137 > 0.01 0/56 > 0.001 8/56 | Coalitional Manipulation vs. Coalitional 2025 0.00133 > 0.01 0/56 > 0.001 2/56 | ||||
| Uncovered set I | Coalitional Manipulation vs. Individual Manipulation 0.00122 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00163 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00157 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00167 > 0.01 0/39 > 0.001 7/39 Coalitional Manipulation vs. Coalitional 2025 0.0022 > 0.01 0/54 > 0.001 9/54 Individual Manipulation vs. Coalitional 2025 0.00172 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.0014 > 0.01 0/56 > 0.001 10/56 | Coalitional Manipulation vs. Coalitional 2025 0.00133 > 0.01 0/56 > 0.001 3/56 | ||||
| Uncovered set II | Coalitional Manipulation vs. Individual Manipulation 0.00165 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Coalitional 2025 0.00152 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00117 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Individual Manipulation 0.00167 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.0022 > 0.01 0/54 > 0.001 9/54 Individual Manipulation vs. Coalitional 2025 0.00148 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Coalitional 2025 0.00136 > 0.01 0/56 > 0.001 9/56 | Coalitional Manipulation vs. Coalitional 2025 0.00133 > 0.01 0/56 > 0.001 4/56 | ||||
| Richelson | Coalitional Manipulation vs. Individual Manipulation 0.00116 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Coalitional 2025 0.00159 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00157 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00167 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Coalitional 2025 0.0022 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00148 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.00143 > 0.01 0/56 > 0.001 10/56 | Coalitional Manipulation vs. Coalitional 2025 0.00151 > 0.01 0/56 > 0.001 4/56 | ||||
| Copeland’s rule I | Coalitional Manipulation vs. Individual Manipulation 0.00198 > 0.01 0/39 > 0.001 7/39 Coalitional Manipulation vs. Coalitional 2025 0.00166 > 0.01 0/54 > 0.001 13/54 Individual Manipulation vs. Coalitional 2025 0.00182 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Individual Manipulation 0.00145 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Coalitional 2025 0.00176 > 0.01 0/54 > 0.001 10/54 Individual Manipulation vs. Coalitional 2025 0.00179 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.00148 > 0.01 0/56 > 0.001 8/56 | Coalitional Manipulation vs. Coalitional 2025 0.00168 > 0.01 0/56 > 0.001 6/56 | ||||
| Copeland’s rule II | Coalitional Manipulation vs. Individual Manipulation 0.00198 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Coalitional 2025 0.00166 > 0.01 0/54 > 0.001 13/54 Individual Manipulation vs. Coalitional 2025 0.00182 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Individual Manipulation 0.00129 > 0.01 0/39 > 0.001 9/39 Coalitional Manipulation vs. Coalitional 2025 0.00176 > 0.01 0/54 > 0.001 10/54 Individual Manipulation vs. Coalitional 2025 0.00179 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.0015 > 0.01 0/56 > 0.001 9/56 | Coalitional Manipulation vs. Coalitional 2025 0.00168 > 0.01 0/56 > 0.001 8/56 | ||||
| Copeland’s rule III | Coalitional Manipulation vs. Individual Manipulation 0.00198 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00166 > 0.01 0/54 > 0.001 11/54 Individual Manipulation vs. Coalitional 2025 0.00182 > 0.01 0/39 > 0.001 2/39 | Coalitional Manipulation vs. Individual Manipulation 0.00152 > 0.01 0/39 > 0.001 4/39 Coalitional Manipulation vs. Coalitional 2025 0.00176 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00179 > 0.01 0/39 > 0.001 3/39 | Coalitional Manipulation vs. Coalitional 2025 0.00148 > 0.01 0/56 > 0.001 7/56 | Coalitional Manipulation vs. Coalitional 2025 0.00168 > 0.01 0/56 > 0.001 5/56 | ||||
| Simpson’s Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00128 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Coalitional 2025 0.00152 > 0.01 0/54 > 0.001 5/54 Individual Manipulation vs. Coalitional 2025 0.00114 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.0019 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00142 > 0.01 0/54 > 0.001 6/54 Individual Manipulation vs. Coalitional 2025 0.00131 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Coalitional 2025 0.00179 > 0.01 0/56 > 0.001 11/56 | Coalitional Manipulation vs. Coalitional 2025 0.00186 > 0.01 0/56 > 0.001 8/56 | ||||
| MinMax procedure | Coalitional Manipulation vs. Individual Manipulation 0.00128 > 0.01 0/39 > 0.001 6/39 | Coalitional Manipulation vs. Individual Manipulation 0.0019 > 0.01 0/39 > 0.001 5/39 | ||||||
| Strong q-Paretian simple majority | Coalitional Manipulation vs. Individual Manipulation 0.00211 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Coalitional 2025 0.00167 > 0.01 0/54 > 0.001 12/54 Individual Manipulation vs. Coalitional 2025 0.00168 > 0.01 0/39 > 0.001 6/39 | Coalitional Manipulation vs. Individual Manipulation 0.00128 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Coalitional 2025 0.00199 > 0.01 0/54 > 0.001 4/54 Individual Manipulation vs. Coalitional 2025 0.00169 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.0016 > 0.01 0/56 > 0.001 5/56 | Coalitional Manipulation vs. Coalitional 2025 0.00121 > 0.01 0/56 > 0.001 1/56 | ||||
| Strong q-Paretian plurality | Coalitional Manipulation vs. Individual Manipulation 0.00232 > 0.01 0/39 > 0.001 7/39 Coalitional Manipulation vs. Coalitional 2025 0.00195 > 0.01 0/54 > 0.001 9/54 Individual Manipulation vs. Coalitional 2025 0.00164 > 0.01 0/39 > 0.001 5/39 | Coalitional Manipulation vs. Individual Manipulation 0.00233 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00199 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00203 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.00159 > 0.01 0/56 > 0.001 3/56 | Coalitional Manipulation vs. Coalitional 2025 0.0014 > 0.01 0/56 > 0.001 4/56 | ||||
| Strongest q-Paretian simple majority | Coalitional Manipulation vs. Individual Manipulation 0.0013 > 0.01 0/39 > 0.001 3/39 Coalitional Manipulation vs. Coalitional 2025 0.00158 > 0.01 0/54 > 0.001 7/54 Individual Manipulation vs. Coalitional 2025 0.00112 > 0.01 0/39 > 0.001 1/39 | Coalitional Manipulation vs. Individual Manipulation 0.00182 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Coalitional 2025 0.00178 > 0.01 0/54 > 0.001 10/54 Individual Manipulation vs. Coalitional 2025 0.00131 > 0.01 0/39 > 0.001 4/39 | Coalitional Manipulation vs. Coalitional 2025 0.00168 > 0.01 0/56 > 0.001 7/56 | Coalitional Manipulation vs. Coalitional 2025 0.00141 > 0.01 0/56 > 0.001 4/56 | ||||
| Threshold Rule | Coalitional Manipulation vs. Individual Manipulation 0.00202 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00226 > 0.01 0/54 > 0.001 12/54 Individual Manipulation vs. Coalitional 2025 0.00143 > 0.01 0/39 > 0.001 6/39 | Coalitional Manipulation vs. Individual Manipulation 0.00201 > 0.01 0/39 > 0.001 5/39 Coalitional Manipulation vs. Coalitional 2025 0.00226 > 0.01 0/54 > 0.001 13/54 Individual Manipulation vs. Coalitional 2025 0.00143 > 0.01 0/39 > 0.001 6/39 | Coalitional Manipulation vs. Coalitional 2025 0.00171 > 0.01 0/56 > 0.001 11/56 | Coalitional Manipulation vs. Coalitional 2025 0.00171 > 0.01 0/56 > 0.001 11/56 | ||||
| Nanson's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00249 > 0.01 0/39 > 0.001 15/39 Coalitional Manipulation vs. Coalitional 2025 0.00149 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00247 > 0.01 0/39 > 0.001 10/39 | Coalitional Manipulation vs. Individual Manipulation 0.00273 > 0.01 0/39 > 0.001 9/39 Coalitional Manipulation vs. Coalitional 2025 0.00176 > 0.01 0/54 > 0.001 3/54 Individual Manipulation vs. Coalitional 2025 0.0026 > 0.01 0/39 > 0.001 10/39 | Coalitional Manipulation vs. Coalitional 2025 0.0014 > 0.01 0/56 > 0.001 7/56 | Coalitional Manipulation vs. Coalitional 2025 0.00131 > 0.01 0/56 > 0.001 6/56 | ||||
| Inverse Borda's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00254 > 0.01 0/39 > 0.001 16/39 Coalitional Manipulation vs. Coalitional 2025 0.00149 > 0.01 0/54 > 0.001 9/54 Individual Manipulation vs. Coalitional 2025 0.00253 > 0.01 0/39 > 0.001 13/39 | Coalitional Manipulation vs. Individual Manipulation 0.00228 > 0.01 0/39 > 0.001 13/39 Coalitional Manipulation vs. Coalitional 2025 0.0013 > 0.01 0/54 > 0.001 4/54 Individual Manipulation vs. Coalitional 2025 0.00213 > 0.01 0/39 > 0.001 13/39 | Coalitional Manipulation vs. Coalitional 2025 0.00151 > 0.01 0/56 > 0.001 3/56 | Coalitional Manipulation vs. Coalitional 2025 0.00116 > 0.01 0/56 > 0.001 1/56 | ||||
| Hare's Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00225 > 0.01 0/39 > 0.001 9/39 Coalitional Manipulation vs. Coalitional 2025 0.00144 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00267 > 0.01 0/39 > 0.001 11/39 | Coalitional Manipulation vs. Individual Manipulation 0.00203 > 0.01 0/39 > 0.001 8/39 Coalitional Manipulation vs. Coalitional 2025 0.00157 > 0.01 0/54 > 0.001 8/54 Individual Manipulation vs. Coalitional 2025 0.00255 > 0.01 0/39 > 0.001 11/39 | Coalitional Manipulation vs. Coalitional 2025 0.00154 > 0.01 0/56 > 0.001 6/56 | Coalitional Manipulation vs. Coalitional 2025 0.0015 > 0.01 0/56 > 0.001 5/56 | ||||
| 1-stable set | Coalitional Manipulation vs. Coalitional 2025 0.00141 > 0.01 0/54 > 0.001 7/54 | Coalitional Manipulation vs. Coalitional 2025 0.00161 > 0.01 0/54 > 0.001 9/54 | Coalitional Manipulation vs. Coalitional 2025 0.00147 > 0.01 0/56 > 0.001 8/56 | Coalitional Manipulation vs. Coalitional 2025 0.00217 > 0.01 0/56 > 0.001 6/56 | ||||
| 2-stable set | Coalitional Manipulation vs. Coalitional 2025 0.00133 > 0.01 0/54 > 0.001 5/54 | Coalitional Manipulation vs. Coalitional 2025 0.00215 > 0.01 0/54 > 0.001 9/54 | Coalitional Manipulation vs. Coalitional 2025 0.00136 > 0.01 0/56 > 0.001 8/56 | Coalitional Manipulation vs. Coalitional 2025 0.00145 > 0.01 0/56 > 0.001 3/56 | ||||
| 3-stable set | Coalitional Manipulation vs. Coalitional 2025 0.00141 > 0.01 0/54 > 0.001 7/54 | Coalitional Manipulation vs. Coalitional 2025 0.00161 > 0.01 0/54 > 0.001 7/54 | Coalitional Manipulation vs. Coalitional 2025 0.00147 > 0.01 0/56 > 0.001 8/56 | Coalitional Manipulation vs. Coalitional 2025 0.00217 > 0.01 0/56 > 0.001 4/56 | ||||
| Approval q=3 | Coalitional Manipulation vs. Individual Manipulation 0.00206 > 0.01 0/39 > 0.001 9/39 Coalitional Manipulation vs. Coalitional 2025 0.0016 > 0.01 0/54 > 0.001 10/54 Individual Manipulation vs. Coalitional 2025 0.00229 > 0.01 0/39 > 0.001 7/39 | Coalitional Manipulation vs. Individual Manipulation 0.00203 > 0.01 0/39 > 0.001 6/39 Coalitional Manipulation vs. Coalitional 2025 0.00165 > 0.01 0/54 > 0.001 9/54 Individual Manipulation vs. Coalitional 2025 0.00226 > 0.01 0/39 > 0.001 6/39 | Coalitional Manipulation vs. Coalitional 2025 0.00242 > 0.01 0/56 > 0.001 11/56 | Coalitional Manipulation vs. Coalitional 2025 0.00267 > 0.01 0/56 > 0.001 10/56 | ||||
| Coombs' Procedure | Coalitional Manipulation vs. Individual Manipulation 0.00325 > 0.01 0/39 > 0.001 11/39 Coalitional Manipulation vs. Coalitional 2025 0.00168 > 0.01 0/54 > 0.001 9/54 Individual Manipulation vs. Coalitional 2025 0.00254 > 0.01 0/39 > 0.001 15/39 | Coalitional Manipulation vs. Individual Manipulation 0.00244 > 0.01 0/39 > 0.001 12/39 Coalitional Manipulation vs. Coalitional 2025 0.00168 > 0.01 0/54 > 0.001 9/54 Individual Manipulation vs. Coalitional 2025 0.00235 > 0.01 0/39 > 0.001 13/39 | Coalitional Manipulation vs. Coalitional 2025 0.00145 > 0.01 0/56 > 0.001 6/56 | Coalitional Manipulation vs. Coalitional 2025 0.00153 > 0.01 0/56 > 0.001 8/56 | ||||